| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Linear modelling problems |
| Difficulty | Easy -1.3 This is a straightforward linear modelling question requiring only basic algebra: finding gradient from two points, then using y = mx + c. Parts (b) and (c) involve simple substitution and a qualitative comment. Significantly easier than average A-level questions as it requires no calculus, no problem-solving insight, just routine application of GCSE-level linear equations. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03c Straight line models: in variety of contexts |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Uses or implies \(V = at + b\) | B1 | Must be \(V = f(t)\) |
| Uses both \(4 = 24a + b\) and \(2.8 = 60a + b\) to get either \(a\) or \(b\) | M1 | Awarded for translating problem and starting to solve; may see \(\pm\frac{4-2.8}{60-24}\) |
| Uses both equations to get both \(a\) and \(b\) | M1 | |
| \(V = -\frac{1}{30}t + 4.8\) | A1 | Or exact equivalent, e.g. \(30V + t = 144\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| (i) States initial volume is \(4.8\ \text{m}^3\) | B1ft | Follow through on their \(b\) |
| (ii) Attempts to solve \(0 = -\frac{1}{30}t + 4.8\) | M1 | States \(V = 0\) and finds \(t\) |
| States 144 minutes | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| States any logical reason, e.g. tank leaks more quickly at start due to greater water pressure; hole may get larger; sediment could plug the hole | B1 | Must give a statement and a matching reason |
## Question 3:
**Part (a):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| Uses or implies $V = at + b$ | B1 | Must be $V = f(t)$ |
| Uses both $4 = 24a + b$ and $2.8 = 60a + b$ to get either $a$ or $b$ | M1 | Awarded for translating problem and starting to solve; may see $\pm\frac{4-2.8}{60-24}$ |
| Uses both equations to get both $a$ and $b$ | M1 | |
| $V = -\frac{1}{30}t + 4.8$ | A1 | Or exact equivalent, e.g. $30V + t = 144$ |
**Part (b):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| (i) States initial volume is $4.8\ \text{m}^3$ | B1ft | Follow through on their $b$ |
| (ii) Attempts to solve $0 = -\frac{1}{30}t + 4.8$ | M1 | States $V = 0$ and finds $t$ |
| States 144 minutes | A1 | |
**Part (c):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| States any logical reason, e.g. tank leaks more quickly at start due to greater water pressure; hole may get larger; sediment could plug the hole | B1 | Must give a statement and a matching reason |
---\begin{enumerate}
\item A tank, which contained water, started to leak from a hole in its base.
\end{enumerate}
The volume of water in the tank 24 minutes after the leak started was $4 \mathrm {~m} ^ { 3 }$
The volume of water in the tank 60 minutes after the leak started was $2.8 \mathrm {~m} ^ { 3 }$
The volume of water, $V \mathrm {~m} ^ { 3 }$, in the tank $t$ minutes after the leak started, can be described by a linear model between $V$ and $t$.\\
(a) Find an equation linking $V$ with $t$.
Use this model to find\\
(b) (i) the initial volume of water in the tank,\\
(ii) the time taken for the tank to empty.\\
(c) Suggest a reason why this linear model may not be suitable.
\hfill \mbox{\textit{Edexcel AS Paper 1 Q3 [8]}}